Understanding Solutions to Systems of Equations

The video tutorial explains how to determine if an ordered pair is a solution to a system of equations. It begins with two equations and checks if the ordered pair (2, 3) satisfies both. The pair works for both equations, confirming it as a solution. A new example is introduced with different equations and the ordered pair (4, -2). The pair satisfies the first equation but not the second, indicating it is not a solution. The tutorial emphasizes the importance of verifying ordered pairs with all equations in a system.

What are the two equations given in the problem?

• 2x + y = 7 and 3x + 5y = 21

• x + y = 7 and 2x + 3y = 21

• x + 2y = 7 and 3x + 5y = 21

• 2x + 3y = 7 and 3x + y = 21

What is the x-value in the ordered pair (2, 3)?

• 7

• 5

• 3

• 2

What is the result of substituting x = 2 and y = 3 into the first equation?

• 7

• 8

• 5

• 6

What is the result of substituting x = 2 and y = 3 into the second equation?

• 21

• 18

• 19

• 20

What is the new ordered pair introduced in the second problem?

• (5, -4)

• (4, -2)

• (3, -1)

• (2, -3)

What is the result of substituting x = 4 and y = -2 into the first new equation?

• 17

• 14

• 15

• 16

What is the result of substituting x = 4 and y = -2 into the second new equation?

• -4

• -3

• -2

• -1

Why is the ordered pair (4, -2) not a solution to the new system of equations?

• It satisfies only the second equation.

• It satisfies neither equation.

• It satisfies only the first equation.

• It satisfies both equations.

What operation is performed first when substituting values into an equation?

• Subtraction

• Division

• Addition

• Multiplication

What is the purpose of substituting an ordered pair into a system of equations?

• To calculate the intercept

• To determine if it is a solution

• To simplify the equation

• To find the slope